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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (6): 9-17.doi: 10.6040/j.issn.1671-9352.0.2022.260

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概率q阶犹豫模糊TODIM方法及其应用

周宇1,2,3(),周礼刚1,2,3,*(),林志超2,3,徐鑫2,3   

  1. 1. 安徽大学大数据与统计学院，安徽 合肥 230601
    2. 安徽大学数学科学学院，安徽 合肥 230601
    3. 安徽大学应用数学中心，安徽 合肥 230601
  • 收稿日期:2022-04-09 出版日期:2023-06-20 发布日期:2023-05-23
  • 通讯作者: 周礼刚 E-mail:1439552596@qq.com;shuiqiaozlg@126.com
  • 作者简介:周宇(1997—), 男, 硕士研究生, 研究方向为统计预测和决策. E-mail: 1439552596@qq.com
  • 基金资助:
    国家自然科学基金资助项目(62276146);国家自然科学基金资助项目(72171002);国家自然科学基金资助项目(71771001);安徽省自然科学基金杰出青年基金资助项目(1908085J03);安徽省学术和技术带头人及后备人选资助项目(2018H179);安徽省高校学科(专业)拔尖人才学术资助项目(gxbjZD2020056)

Probabilistic q-rung hesitant fuzzy TODIM method and its application

Yu ZHOU1,2,3(),Ligang ZHOU1,2,3,*(),Zhichao LIN2,3,Xin XU2,3   

  1. 1. School of Big Data and Statistics, Anhui University, Hefei 230601, Anhui, China
    2. School of Mathematical Sciences, AnhuiUniversity, Hefei 230601, Anhui, China
    3. Anhui Center for Applied Mathematics, Anhui University, Hefei 230601, Anhui, China
  • Received:2022-04-09 Online:2023-06-20 Published:2023-05-23
  • Contact: Ligang ZHOU E-mail:1439552596@qq.com;shuiqiaozlg@126.com

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摘要：

为了度量概率q阶犹豫模糊信息之间的差异, 基于得分函数和综合犹豫度提出一种概率q阶犹豫模糊距离测度, 并研究其性质。进而, 基于概率q阶犹豫模糊距离测度, 提出一种概率q阶犹豫模糊交互式多准则决策(TOmada de decisão interative multicritério, TODIM)方法。最后通过实例说明所提出的TODIM方法的合理性和有效性, 并进行灵敏度分析。

关键词: 概率q阶犹豫模糊集, 距离测度, TODIM, 多属性决策

Abstract:

To measure differences in probabilistic q-rung hesitant fuzzy information, a novel measure of the probabilistic q-rung hesitant fuzzy distance is proposed based on the score function and overall hesitancy. The properties of this measure are discussed. A probabilistic q-rung hesitant fuzzy TODIM method is proposed based on the new distance measure. Finally, a practical example is presented to illustrate the reasonableness and effectiveness of the proposed method, and a sensitivity analysis is performed.

Key words: probabilistic q-rung hesitant fuzzy set, distance measure, TODIM, multi-attribute decision-making

中图分类号: 

  • O159

表1

概率$q$阶犹豫模糊决策矩阵$\widetilde{\boldsymbol{R}}=\left(\tilde{r}_{i j}\right)_{5 \times 4}$"

C1 C2 C3 C4
X1 {〈0.5, 0.2〉(0.6),
〈0.6, 0.3〉(0.4)}		 {〈0.4, 0.3〉(1)} {〈0.2, 0.5〉(0.3),
〈0.3, 0.6〉(0.7)}		 {〈0.6, 0.1〉(0.5),
〈0.7, 0.2〉(0.5)}
X2 {〈0.3, 0.3〉(0.3),
〈0.5, 0.3〉(0.4),
〈0.5, 0.4〉(0.3)}		 {〈0.5, 0.1〉(0.3),
〈0.6, 0.2〉(0.5),
〈0.7, 0.1〉(0.2)}		 {〈0.4, 0.2〉(0.5),
〈0.5, 0.2〉(0.3),
〈0.6, 0.3〉(0.2)}		 {〈0.5, 0.2〉(0.6)
〈0.7, 0.2〉(0.4)}
X3 {〈0.3, 0.2〉(0.4),
〈0.7, 0.2〉(0.6)}		 {〈0.6, 0.2〉(0.5),
〈0.7, 0.2〉(0.5)}		 {〈0.1, 0.3〉(0.2),
〈0.2, 0.5〉(0.2),
〈0.3, 0.6〉(0.6)}		 {〈0.2, 0.4〉(0.6),
〈0.3, 0.6〉(0.4)}
X4 {〈0.3, 0.2〉(0.4),
〈0.4, 0.3〉(0.3),
〈0.5, 0.3〉(0.3)}		 {〈0.4, 0.1〉(0.6),
〈0.6, 0.3〉(0.4)}		 {〈0.3, 0.3〉(0.4),
〈0.4, 0.4〉(0.6)}		 {〈0.5, 0.1〉(0.6),
〈0.6, 0.2〉(0.4)}
X5 {〈0.3, 0.1〉(0.7),
〈0.5, 0.2〉(0.3)}		 {〈0.4, 0.1〉(0.6),
〈0.6, 0.3〉(0.4)}		 {〈0.3, 0.5〉(0.4),
〈0.4, 0.2〉(0.2),
〈0.5, 0.2〉(0.4)}		 {〈0.5, 0.2〉(1)}

表2

规范化决策矩阵R =(rij)5×4"

C1 C2 C3 C4
X1 {〈0.5, 0.2〉(0.6),
〈0.5, 0.2〉(0),
〈0.6, 0.3〉(0.4)}		 {〈0.4, 0.3〉(0),
〈0.4, 0.3〉(0),
〈0.4, 0.3〉(1)}		 {〈0.3, 0.6〉(0.7),
〈0.2, 0.5〉(0),
〈0.2, 0.5〉(0.3)}		 {〈0.6, 0.1〉(0.5),
〈0.6, 0.1〉(0),
〈0.7, 0.2〉(0.5)}
X2 {〈0.3, 0.3〉(0.3),
〈0.5, 0.4〉(0.3),
〈0.5, 0.3〉(0.4)}		 {〈0.5, 0.1〉(0.3),
〈0.6, 0.2〉(0.5),
〈0.7, 0.1〉(0.2)}		 {〈0.4, 0.2〉(0.5),
〈0.5, 0.2〉(0.3),
〈0.6, 0.3〉(0.2)}		 {〈0.5, 0.2〉(0.6)
〈0.5, 0.2〉(0),
〈0.7, 0.2〉(0.4)}
X3 {〈0.3, 0.2〉(0.4),
〈0.3, 0.2〉(0),
〈0.7, 0.2〉(0.6)}		 {〈0.6, 0.2〉(0.5),
〈0.6, 0.2〉(0),
〈0.7, 0.2〉(0.5)}		 {〈0.3, 0.6〉(0.6),
〈0.2, 0.5〉(0.2),
〈0.1, 0.3〉(0.2)}		 {〈0.3, 0.6〉(0.4),
〈0.2, 0.4〉(0),
〈0.2, 0.4〉(0.6)}
X4 {〈0.3, 0.2〉(0.4),
〈0.4, 0.3〉(0.3),
〈0.5, 0.3〉(0.3)}		 {〈0.4, 0.1〉(0.6),
〈0.4, 0.1〉(0),
〈0.6, 0.3〉(0.4)}		 {〈0.3, 0.3〉(0.4),
〈0.3, 0.3〉(0),
〈0.4, 0.4〉(0.6)}		 {〈0.5, 0.1〉(0.6),
〈0.5, 0.1〉(0),
〈0.6, 0.2〉(0.4)}
X5 {〈0.3, 0.1〉(0.7),
〈0.3, 0.1〉(0),
〈0.5, 0.2〉(0.3)}		 {〈0.4, 0.1〉(0.6),
〈0.4, 0.1〉(0),
〈0.6, 0.3〉(0.4)}		 {〈0.3, 0.5〉(0.4),
〈0.4, 0.2〉(0.2),
〈0.5, 0.2〉(0.4)}		 {〈0.5, 0.2〉(0),
〈0.5, 0.2〉(0),
〈0.5, 0.2〉(1)}

图1

ξi关于不同参数值q的变化图"

图2

ξi关于不同参数值θ的变化图"

1 ZADEHL A .Fuzzy sets[J].Information and Control,1965,8(3):338-353.
doi: 10.1016/S0019-9958(65)90241-X
2 ATANASSOVK T .Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87-96.
doi: 10.1016/S0165-0114(86)80034-3
3 XUZeshui .Intuitionistic fuzzy aggregation operators[J].IEEE Transactions on Fuzzy Systems,2007,15(6):1179-1187.
doi: 10.1109/TFUZZ.2006.890678
4 YAGER R R. Pythagorean fuzzy subsets[C]// IFSA World Congress and NAFIPS Annual Meeting. Edmonton, Canada: IEEE, 2013: 57-61.
5 YAGERR R .Generalized fuzzy sets[J].IEEE Transactions on Fuzzy Systems,2017,25(5):1222-1230.
doi: 10.1109/TFUZZ.2016.2604005
6 LIUPeide , WANGPeng .Some q-rung orthopair fuzzy aggregation operators and their applications to multiple attribute decision making[J].International Journal of Intelligent Systems,2017,33(2):259-280.
7 TORRAV .Hesitant fuzzy sets[J].International Journal of Intelligent Systems,2010,25(6):529-539.
8 朱斌. 基于偏好关系的决策方法研究及应用[D]. 南京: 东南大学, 2014.
ZHU Bin. Decision making methods and applications based on preference relations[D]. Nanjing: Southeast University, 2014.
9 LIUDonghai , PENGDan , LIUZaiming .The distance measures between q-rung hesitant fuzzy sets and their application in multiple criteria decision making[J].International Journal of Intelligent Systems,2019,34(9):2104-2121.
doi: 10.1002/int.22133
10 尹文静, 郑婷婷, 李龙妹.概率q阶犹豫模糊熵及其应用[J].郑州大学学报(理学版),2020,52(4):75-81.
YINWenjing , ZHENGTingting , LILongmei .Probabilistic q-rung orthopair hesitant fuzzy entropy and its application[J].Journal of Zhengzhou University(Natural Science Edition),2020,52(4):75-81.
11 GRZEGORZEWSKIP .Distances between intuitionistic fuzzy sets and interval-valued fuzzy sets based on the Hausdorff distance[J].Fuzzy Sets and Systems,2004,148(2):319-328.
doi: 10.1016/j.fss.2003.08.005
12 HUANGWenliang , YANGMinshen .Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance[J].Pattern Recognition Letters,2004,25(14):1603-1611.
doi: 10.1016/j.patrec.2004.06.006
13 XUZeshui .Deviation measures of linguistic preference relations in group decision making[J].Omega,2005,33(3):249-254.
doi: 10.1016/j.omega.2004.04.008
14 DINGJie , XUZeshui , ZHAONa .An interactive approach to probabilistic hesitant fuzzy multi-attribute group decision making with incomplete weight information[J].Journal of Intelligent & Fuzzy Systems,2017,32(3):2523-2536.
15 GOMESL , LIMAM .TODIM: basics and application to multicriteria ranking of projects with environmental impacts[J].Foundations of Computing and Decision Sciences,1991,16(3):113-127.
16 ZHANGDong , LIYongli , WUChong .An extended TODIM method to rank products with online reviews under intuitionistic fuzzy environment[J].Journal of the Operational Research Society,2020,71(2):322-334.
doi: 10.1080/01605682.2018.1545519
17 QINQuande , LIANGFuqi , LILi ,et al.A TODIM-based multi-criteria group decision making with triangular intuitionistic fuzzy numbers[J].Applied Soft Computing,2017,55(6):93-107.
18 刘熠, 秦亚, 刘好斌,等.广义q-ROF TODIM方法及应用[J].控制与决策,2020,35(8):2021-2028.
LIUYi , QINYa , LIUHaobin ,et al.Generalized q-ROF TODIM method and its application[J].Control and Decision,2020,35(8):2021-2028.
19 周延年, 徐彤, 胡滨.属性相关条件下广义q-ROF TODIM决策方法[J].西北工业大学学报,2020,38(5):1068-1073.
doi: 10.3969/j.issn.1000-2758.2020.05.021
ZHOUYannian , XUTong , HUBin .Generalized q-ROF TODIM decision-making method considering attribute correlation[J].Journal of Northwestern Polytechnical University,2020,38(5):1068-1073.
doi: 10.3969/j.issn.1000-2758.2020.05.021
20 TIANXiaoli , NIUMeiling , ZHANGWeike .A novel TODIM based on prospect theory to select green supplier with q-rung fuzzy set[J].Technological and Economic Development of Economy,2021,27(2):284-310.
21 ZHANGXiaolu , XUZeshui .The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment[J].Knowledge-Based Systems,2014,61(1):48-58.
22 孔令艳, 谭倩云.犹豫模糊语言TODIM法及其应用[J].统计与决策,2017,(5):98-100.
doi: 10.13546/j.cnki.tjyjc.2017.05.023
KONGLingyan , TANQianyun .Hesitant fuzzy linguistic TODIM decision making method and its application[J].Statistics and Decision,2017,(5):98-100.
doi: 10.13546/j.cnki.tjyjc.2017.05.023
23 SONGHaifeng , CHENZichun .Multi-attribute decision-making method based distance and COPRAS method with probabilistic hesitant fuzzy environment[J].International Journal of Computational Intelligence Systems,2021,14(1):1229-1241.
doi: 10.2991/ijcis.d.210318.001
24 XUZeshui , XIAMeimei .Distance and similarity measures for hesitant fuzzy sets[J].Information Sciences,2011,181(11):2128-2138.
doi: 10.1016/j.ins.2011.01.028
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